One of the first questions to ask is what exactly is the statistic that we're looking at. Judge Sotomayor has been on the 2d Circuit bench for 11 years, and in that time has heard nearly 3000 cases. Only in the more controversial cases is a published opinion typically issued, and she has published 232 opinions. Of those 232, five of them have been reviewed by the Supreme Court. And of those five, three have been overturned. So you could say that 60% of her reviewed opinions were overturned, but you could also say that 2% of her published opinions have been overturned, or that 0.2% of her total decisions have been overturned.
The other more relevant question to ask is how her statistics compare with her colleagues. Here it's useful to note that the Supreme Court only grants review of about 1% of the appeals filed, and the Court, in order to use its time wisely, only grants review to those cases where there is inconsistency across the Circuits, or where they expect to clarify or revise the precedent. In other words, the high court is likely to overturn the cases it selects for review, because it selects the controversial ones. According to statistics compiled by SCOTUSblog, since 2004, the Supreme Court has reversed 73% of the cases it reviewed. So it turns out that Sotomayor's 60% reversal rate is better than average. As Rachel Maddow observed, this is comparable to batting averages, where Sotomayor has a .400 "batting average". That's considered quite good. It has also been observed that Justice Alito, at the time of his Supreme Court confirmation, had a 100% reversal rate.
Knowledgeable attorneys observe that a judge's reversal rate is not a very meaningful statistic. In other words, the critics are clutching at straws here.
University of Chicago Law professor Eric Posner has been analyzing other comparative data about appellate judges, including how often their opinions are cited in other opinions or in law review articles (a measure of their influence and respect of their peers) and how often they have dissented in panel decisions (a measure of how inline with their colleagues they are). His conclusion:
the data should put to rest the rumor that Judge Sotomayor is not a competent jurist. She holds her own among a highly respected group... If citations reflect quality, Sotomayor may well be one of the top appellate judges in the country.